Peter S. Erbach

Optical wavelet transform by the phase-only joint-transform correlator

A method is presented that performs the optical wavelet transform with liquid-crystal televisions as spatial light modulators operating only on the phase of the incident coherent light. The architecture is the joint-transform correlator, and the wavelets and the image to be transformed are encoded in the input plane of the system. The mathematical formalism describing the adaptation of the joint-transform correlator to the wavelet transform is given and extended to the operation of the phase-only joint-transform correlator. A new wavelet is described for two-dimensional image processing, and experimental results are presented for optical wavelet transforms done in real time by use of this wavelet in the phase-only joint-transform-correlator architecture. The analysis is extended to multiwavelet (multispectral) analysis by the joint-transform correlator, and simulation results are given. Finally experimental results with the phase-only joint-transform correlator applied to multi-wavelet analysis are presented.

Spatial light modulator phase depth determination from optical diffraction information

A noninterferometric technique is presented for determining the phase modulating characteristics of spatial light modulators. Examining the far-field diffraction pattern intensity distribution for specific input functions enables the phase modulation to be calculated. Results are compared with usual interferometric techniques for a liquid crystal based modulator.

Optical recognition of phase-encrypted biometrics

An optical security system using phase encryption of biometric identification data is demonstrated. For this effort, fingerprints are used as the biometric signature. Two types of phase masks are fabricated: photopolymer film and polyimide film. The masks containing the phase-encrypted fingerprints are tested using a joint transform optical correlator. The results of the tests demonstrate that the encryption methods are successful, as the target fingerprint is recognized and the test print is rejected.

Phase-only joint-transform correlator: analysis and experimental results

An analysis of the popular joint-transform optical correlator is presented for architectures employing spatial light modulators that operate only on the phase of the coherent light. Experimental results are also presented, for simple scenes that produce analytic solutions, which support the analysis.

Wavelet transform applied to synthetic aperture radar - optical implementation and adaptive techniques

The wavelet transform is applied to signal processing of synthetic aperture radar and techniques for determining the range, cross-range, and rotation of the target as well as adaptive process for better resolution are studied. We also optically implement the wavelet transform in the laboratory for real-time processing of radar data, and describe methods for adaptive processing.

Clutter reduction and target detection enhancement using wavelet transform techniques

In this paper, a multichannel optical wavelet processor and a matching pursuit processor capable of enhancing the detection of cluttered targets are presented. Wavelet functions have zero-mean and are virtually band-pass filters. In many cases, targets and clutter are separable in the spatial spectral domain. Therefore, by selecting wavelet functions that represent features of targets but are insensitive to that of clutter, targets can be extracted from the input scene while clutter is suppressed. Due to dyadic sampling, a multichannel optical wavelet processor with a limited number of channels can detect regions of interest for different targets. With matching pursuit decomposition, features of targets are extracted and represented in a few wavelets known as coherent structure; whereas clutter and noise are diluted across the dictionary. Clutter and noise can then be effectively removed from the signal by a simple thresholding operation. A time-frequency energy distribution can be derived from matching pursuit decomposition, which contains no interference terms and thus clearly characterized the input signal in the time-frequency plane. Optical architectures of these processors are described. Simulated and experimental results are provided.

Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators

Interferometric techniques have been employed by a number of investigators to determine the phase modulating characteristics of popular spatial light modulators. The technique works well but requires the set-up and operation of a sensitive interferometer. A non-interferometric technique is presented for determining the phase modulating characteristics of spatial light modulators. Examining the far field diffraction pattern distribution for specific input functions allows the phase modulation to be calculated. The degree of phase modulation appears in the Fourier transform as an intensity modulation which can be measured. Results are compared with usual interferometric techniques for a liquid crystal based modulator.

Turbulence simulation and optical processing through turbulent media

Experimental investigating the possibility of optical processing through turbulent media were investigated and a model for turbulence is discussed. A technique for creating an optical device to display the turbulence model real-time is introduced and a technique for removing the turbulence is demonstrated.

Scale invariant optical Mellin-wavelet joint transform correlation

This paper discusses the combination of the wavelet transform with the scale invariant Mellin transform in an optical joint transform correlator (JTC) architecture. A mathematical and numerical analysis are presented with three optical designs for performing the Mellin-wavelet joint transform.

Application of wavelet transform to synthetic aperture radar and its optical implementation

The wavelet transform is applied to signal processing of synthetic aperture radar, and techniques for determining the range, cross-range, and rotation of the target are studied. The wavelet transform was also implemented optically in the laboratory for real-time processing of the radar data.